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On the expressiveness of frame satisfiability and fragments of second-order logic

Published online by Cambridge University Press:  12 March 2014

Thomas Eiter  and
Georg Gottlob
Thomas Eiter
Affiliation:
Information Systems Department, Tu Vienna, Paniglgasse 16, A-1040, Wien, Austria, E-mail: eiter@dbai.tuwien.ac.at
Georg Gottlob
Affiliation:
Information Systems Department, Tu Vienna, Paniglgasse 16, A-1040, Wien, Austria, E-mail: gottlob@dbai.tuwien.ac.at
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Abstract

It was conjectured by Halpern and Kapron (Annals of Pure and Applied Logic, vol. 69, 1994) that frame satisfiability of propositional modal formulas is incomparable in expressive power to both (Ackermann) and (Bernays-Schönfinkel). We prove this conjecture. Our results imply that (Ackermann) and (Bernays-Schönfinkel) are incomparable in expressive power, already on finite graphs. Moreover, we show that on ordered finite graphs, i.e., finite graphs with a successor, (Bernays-Schönfinkel) is strictly more expressive than (Ackermann).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 1 , March 1998 , pp. 73 - 82
Copyright
Copyright © Association for Symbolic Logic 1998

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